Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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The Influence of a Slowly Oscillating Movement on the Velocity Potential
The Influence of a Slowly Oscillating Movement on the Velocity Potential
Pages 119-132
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From page 119... ...
710 ~1 L H x z n Fn G F.S. c' a Tn Jn7 Kn, Yn Beam at midship Wetted surface area at rest Ship speed Ship block coefficient Gravitational acceleration Pressure Wave elevation along hull steady wave elevation unsteady wave elevation Oscillator amplitude Length at water line Draft at midship coordinate system moving with velocity U in forward direction vertically upward unit vector normal to ~ in outward direction Froude number(U/~)
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From page 120... ...
The formulation will be done in a Cartesian coordinate system moving with the object. With the x coordinate in forward direction and the z coordinate vertically upward.
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From page 121... ...
denotes a linear differential operator acting on a. 3 The leading equations 3.1 Calculation of the singularity distributions Introduction of a Green's function G and application of Green's theorem to the domain as can be seen in figure 3.1.
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~: if the density a of the distribution on ~ is continuous at x, the normal derivative of the potential ~ approaches limits as X approaches x along the normal to ~ at x from either side.
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In this scheme use has been made of the numerical evaluation of the wave resistance Green function as done by Newman (~11~+ t12~)
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From page 124... ...
4 The Green's function 4.1 Behavior of the Green's function. In Wehausen and Laitone t14]
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From page 125... ...
has written two papers in the Journal of Ship research about the evaluation of the wave resistance Green function: one of of the calculation of the double integral and one for the calculation of the single integral on the centerplane. The Green function is written in the following form (see Wehausen and Laitone t14~: 1 1 Tn(X)
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From page 126... ...
An example for the Green function can be seen in figure 4.8 . The wave character is well observed here.
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From page 127... ...
So the Pade approximants seems worse here. The Euler function evaluated at x = 1 is wildly oscillating ( when using Taylor expansion)
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From page 128... ...
. -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Figure 6.3: Hull side wave profiles of WIGLEY.
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From page 129... ...
will be calculated. The Wigley Hull is a mathematically defined form (see figure 6.1~: y = By _ `227~2~1 _ ~ Z >~2~ with -2 |
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~ _A 6 2 o -2 4 ~ -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 . v 0 ~ ~ -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Figure 6.6: Wave heights for the unsteady motion (En = 0.31)
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From page 131... ...
The potential function, source strength and Green function are expanded in the small parameter w. A first order approximation for the unsteady wave have been obtained using calculation that only involves the evolution of the steady wave Green function.
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From page 132... ...
and Kajitani, H., 'Computations of wave resistance by the low speed theory imposing accurate hull surface condition', Proc. Workshop on Ship WaveResistance Comp., Bethesda, Marylalld (1979)
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